BeamBeam Simulations for Crab Waist Scheme Dmitry Shatilov

Beam-Beam Simulations for Crab Waist Scheme Dmitry Shatilov BINP, Novosibirsk X Subep. B General Meeting, SLAC, 09 October 2009 1

Outline § Weak-Strong beam-beam simulations with “crabbed” beams § Crabbed beam: pictures § Geometrical luminosity: comparison with analytical calculations § Comparison with DAΦNE experimental results § Simulations for Super. B with linear lattice § Summary 2

Crabbed Strong Beam distribution is non-Gaussian due to the crab sextupoles, even without beam-beam, so the Bassetti-Erskine formulae are not valid. In my old simulations I used these formulae, as I had no other choice. So, the “weak” beam was crabbed, while the “strong” one was Gaussian. Imperfections of this approach were recognized from the very beginning. Correct simulations with the crabbed “strong” beam require that the beam kicks are calculated using the grids, as there are no corresponding analytical formulae. Recently this new feature has been implemented in LIFETRAC. In principle it allows calculating beam-beam kicks from arbitrary “strong” bunch distribution, and can be used in future for quasi strong-strong simulations. 3

Crabbed Strong Beam (DAΦNE parameters), Pictures: Log (dens) ( Gaussian, Z=0 Crabbed, Z=1 cm 4 Crabbed, Z=0 Crabbed, Z=2 cm

Crabbed Strong Beam (DAΦNE parameters), Pictures: Vertical kick ( Fy (Gaussian, Z=2 cm) Fy (Gaussian, Y= -0. 5 σy) Fy (Crabbed, Z=2 cm) Fy (Crabbed, Y= -0. 5 σy) 5

Geometrical Luminosity Gain Luminosity gain in % Crab=V vs. Gauss Crab=V vs. Crab=1. 0 Crab=V vs. Crab=V V Crab Value (nominal = 1) DAΦNE Siddharta “initial” parameters (βy=0. 65 cm) Lines: analytical calculations by Mathematica, performed by M. Zobov. Markers: tracking results by LIFETRAC. Red and blue points were obtained with the crabbed strong beam. 6

Weak-Strong Simulations vs. Experiment Crab OFF Old program New program Optimal Crab 7

Simulations for Super. B with Linear Lattice Due to asymmetry in emittances and beta-functions between HER and LER the optimum “crab” values are different: 0. 8 for HER and 1. 0 for LER. The designed tune shifts are rather small: ξy < 0. 12, so there is now blowup, but the effect of dynamic beta exists. Plus the geometric luminosity gain due to crab… As a result, the luminosity becomes even higher than the designed value: L ≈ 1. 07· 1036 instead of 1. 02· 1036. HER LER Tunes: (0. 542, 0. 580, 0. 01) Np = 5. 74· 1010 Nb = 1011 The next step: simulations with the real lattice (sextupoles, etc. ). It will be done as soon as the lattice will be finalized and optimized for DA. 8

Summary § Crabbed strong beam has been implemented in LIFETRAC and tested. There is a good agreement between simulations and DAΦNE experimental data. § Simulations for Super. B with linear lattice indicated that there are no problems due to beam-beam interaction. Simulations with nonlinear lattice are required to make more accurate predictions. § In general, with the crabbed “strong” beam (new feature) the optimum for “crab” value is increased, but the luminosity and beam tails in the optimum are almost the same as in the old simulations, or even better. It means all the previous simulations are relevant in assumption that the “crab” value (crab sextupole strength) is slightly increased. § The road towards improved quasi strong-strong simulations (actually, it will be strong-strong without coherent effects) is opened and has been already passed by more than 50 %. 9